A318944 Number of Dyck paths with n nodes and altitude 4.

0, 0, 0, 0, 1, 8, 32, 114, 376, 1177, 3549, 10406, 29861, 84249, 234502, 645625, 1761765, 4772534, 12851261, 34434561, 91890118, 244385617, 648139821, 1714976054, 4529163125, 11942440233, 31448759302, 82727323369, 217426319541, 571033273142

Offset

0,6

References

Czabarka, É., Flórez, R., Junes, L., & Ramírez, J. L. (2018). Enumerations of peaks and valleys on non-decreasing Dyck paths. Discrete Mathematics, 341(10), 2789-2807.

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (9,-31,50,-36,8).

Formula

a(n) = 9*a(n-1) - 31*a(n-2) + 50*a(n-3) - 36*a(n-4) + 8*a(n-5) for n>9. - Colin Barker, Apr 11 2019

Maple

(1-x)^2*x^4*(1+x-8*x^2+7*x^3)/(1-2*x)^3/(1-3*x+x^2) ;
taylor(%, x=0, 30) ;
gfun[seriestolist](%) ; # R. J. Mathar, Nov 25 2018

Mathematica

LinearRecurrence[{9, -31, 50, -36, 8}, {0, 0, 0, 0, 1, 8, 32, 114, 376, 1177}, 30] (* Harvey P. Dale, Nov 03 2019 *)

Prog

(PARI) concat([0, 0, 0, 0], Vec(x^4*(1 - x)^2*(1 + x - 8*x^2 + 7*x^3) / ((1 - 2*x)^3*(1 - 3*x + x^2)) + O(x^40))) \\ Colin Barker, Apr 11 2019

Crossrefs

A column of A318942.

Sequence in context: A204643 A036393 A003201 * A196097 A234272 A269077

Adjacent sequences: A318941 A318942 A318943 * A318945 A318946 A318947

Keyword

nonn,easy

Author

N. J. A. Sloane, Sep 18 2018

Status

approved